If you're looking for something different to play, try Catan or Carcassonne. These Xbox Live Arcade titles are based on popular board games. They have similar goals, controlling land or resources to win, but the gameplay is different.
The Xbox Live Arcade title Catan is based on a board game Settlers of Catan. The object of the game is be the first player to collect 10 Victory Points earned by building roads, settlements and cities. Resource cards are used for building those objects and are gained either through a dice roll, trading with other players or stealing.
Carcassonne is based on a board game of the same name. According to the Wikipedia, it is named after the town of Carcassonne in southern France. The object of this game is to place tiles representing roads, fields and city walls together to form cities where residents called followers are then placed. Once all the tiles are used the game ends. Points are tallied based on where followers are located. The person with the most points wins.
If you're looking for something family friendly (neither of these games are violent) and a change of pace from frantic action like Geometry Wars, you should give these games a look.